# ASTM F1321-14

Designation: F1321 − 14 An American National StandardStandard Guide forConducting a Stability Test (Lightweight Survey andInclining Experiment) to Determine the Light ShipDisplacement and Centers of Gravity of a Vessel1This standard is issued under the fixed designation F1321; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.This standard has been approved for use by agencies of the U.S. Department of Defense.INTRODUCTIONThis guide provides the marine industry with a basic understanding of the various aspects of astability test. It contains procedures for conducting a stability test to ensure that valid results areobtained with maximum precision at a minimal cost to owners, shipyards, and the government. Thisguide is not intended to instruct a person in the actual calculation of the light ship displacement andcenters of gravity, but rather to be a guide to the necessary procedures to be followed to gather accuratedata for use in the calculation of the light ship characteristics.Acomplete understanding of the correctprocedures used to perform a stability test is imperative to ensure that the test is conducted properlyand so that results can be examined for accuracy as the inclining experiment is conducted. It isrecommended that these procedures be used on all vessels and marine craft.1. Scope1.1 This guide covers the determination of a vessel’s lightship characteristics. In this standard, a vessel is a traditionalhull-formed vessel. The stability test can be considered to betwo separate tasks; the lightweight survey and the incliningexperiment. The stability test is required for most vessels upontheir completion and after major conversions. It is normallyconducted inshore in calm weather conditions and usuallyrequires the vessel be taken out of service to prepare for andconduct the stability test. The three light ship characteristicsdetermined from the stability test for conventional (symmetri-cal) ships are displacement (“displ”), longitudinal center ofgravity (“LCG”), and the vertical center of gravity (“KG”). Thetransverse center of gravity (“TCG”) may also be determinedfor mobile offshore drilling units (MODUs) and other vesselswhich are asymmetrical about the centerline or whose internalarrangement or outfitting is such that an inherent list maydevelop from off-center weight. Because of their nature, otherspecial considerations not specifically addressed in this guidemay be necessary for some MODUs. This standard is notapplicable to vessels such as a tension-leg platforms, semi-submersibles, rigid hull inflatable boats, and so on.1.2 The limitations of 1 % trim or 4 % heel and so on applyif one is using the traditional pre-defined hydrostatic charac-teristics. This is due to the drastic change of waterplane area. Ifone is calculating hydrostatic characteristics at each move,such as utilizing a computer program, then the limitations arenot applicable.1.3 The values stated in inch-pound units are to be regardedas standard. No other units of measurement are included in thisstandard.1.4 This standard does not purport to address the safetyconcerns, if any, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety andhealth practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:E100 Specification for ASTM Hydrometers3. Terminology3.1 Definitions:3.1.1 inclining experiment—involves moving a series ofweights, in the transverse direction, and then measuring theresulting change in the equilibrium heel angle of the vessel. Byusing this information and applying basic naval architectureprinciples, the vessel’s vertical center of gravity KG is deter-mined.1This guide is under the jurisdiction of ASTM Committee F25 on Ships andMarine Technology and is the direct responsibility of Subcommittee F25.01 onStructures.Current edition approved May 1, 2014. Published May 2014. Originallyapproved in 1990. Last previous edition approved in 2013 as F1321 – 13ε1. DOI:10.1520/F1321-14.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.1.2 Condition 1—vessel in Condition 1 is a vessel com-plete in all respects, but without consumables, stores, cargo,crew and effects, and without any liquids on board exceptmachinery fluids, such as lubricants and hydraulics, are atoperating levels. Condition 1 is sometimes referred to as“operational light ship.”3.1.3 Condition 0—vessel in Condition 0 is a vessel asinclined.3.1.4 lightweight survey—this task involves taking an auditof all items which must be added, deducted, or relocated on thevessel at the time of the stability test so that the observedcondition of the vessel can be adjusted to the light shipcondition. The weight, longitudinal, transverse, and verticallocation of each item must be accurately determined andrecorded. Using this information, the static waterline of theship at the time of the stability test as determined frommeasuring the freeboard or verified draft marks of the vessel,the vessel’s hydrostatic data, and the seawater density; the lightship displacement and longitudinal center of gravity can beobtained. The transverse center of gravity may also becalculated, if necessary.3.1.5 relative density—(formerly known as specificgravity)—ratio of the mass of a given volume of material at astated temperature to the mass of an equal volume gas freedistilled water at the same or different temperatures. Bothreferenced temperatures shall be explicitly stated.4. Significance and Use4.1 From the light ship characteristics one is able to calcu-late the stability characteristics of the vessel for all conditionsof loading and thereby determine whether the vessel satisfiesthe applicable stability criteria.Accurate results from a stabilitytest may in some cases determine the future survival of thevessel and its crew, so the accuracy with which the test isconducted cannot be overemphasized. The condition of thevessel and the environment during the test is rarely ideal andconsequently, the stability test is infrequently conducted ex-actly as planned. If the vessel is not 100 % complete and theweather is not perfect, there ends up being water or shipyardtrash in a tank that was supposed to be clean and dry and soforth, then the person in charge must make immediate deci-sions as to the acceptability of variances from the plan. Acomplete understanding of the principles behind the stabilitytest and a knowledge of the factors that affect the results isnecessary.5. Theory5.1 The Metacenter—(See Fig. 1). The transverse metacen-ter (“M”) is based on the hull form of a vessel and is the pointaround which the vessel’s center of buoyancy (“B”) swings forsmall angles of inclination (0° to 4° unless there are abruptchanges in the shape of the hull). The location of B is fixed forany draft, trim, and heel, but it shifts appreciably as heelincreases. The location of B shifts off the centerline for smallangles of inclination (“θ”), but its height above the molded keel(“K”) will stay essentially the same. The location of M, on theother hand, is essentially fixed over a range of heeling anglesup to about 4°, as the ship is inclined at constant displacementand trim. The height of M above K, known as “KM”, is oftenplotted versus draft as one of the vessel’s curves of form. As ageneral “rule of thumb,” if the difference from the design trimof the vessel is less than 1 % of its length, the KM can be takendirectly from either the vessel’s curves of form or hydrostatictables. Because KM varies with trim, the KM must be com-puted using the trim of the ship at the time of the stability testwhen the difference from the design trim of the vessel is greaterthan 1 % of its length. Caution should be exercised whenapplying the “rule of thumb” to ensure that excessive error, aswould result from a significant change in the waterplane areaduring heeling, is not introduced into the stability calculations.5.2 Metacentric Height—The vertical distance between thecenter of gravity (“G”) and M is called the metacentric height(“GM”). At small angles of heel, GM is equal to the initialslope of the righting arm (“GZ”) curve and is calculated usingthe relationship, GZ = GM sin θ. GM is a measure of vesselstability that can be calculated during an inclining experiment.As shown in Fig. 1 and Fig. 2, moving a weight (“W”) acrossthe deck a distance (“x”) will cause a shift in the overall centerof gravity (G–G ) of the vessel equal to (W)(x)/displ andparallel to the movement of W. The vessel will heel over to anew equilibrium heel angle where the new center of buoyancy,B , will once again be directly under the new center of gravity(G ). Because the angle of inclination during the incliningexperiment is small, the shift in G can be approximated byGMtan θ and then equated to (W)(x)/displ. Rearranging thisequation slightly results in the following equation:FIG. 1 Movement of the Center of BuoyancyFIG. 2 Metacentric HeightF1321 − 142GM 5~W!~x!~displ!~ tan θ!(1)Since GM and displ remain constant throughout the incliningexperiment the ratio (W)(x)/tan θ will be a constant. Bycarefully planning a series of weight movements, a plot oftangents is made at the corresponding moments. The ratio ismeasured as the slope of the best represented straight linedrawn through the plotted points as shown in Fig. 3, wherethree angle indicating devices have been used. This line doesnot necessarily pass through the origin or any other particularpoint, for no single point is more significant than any otherpoint. A linear regression analysis is often used to fit thestraight line.5.3 Calculating the Height of the Center of Gravity Abovethe Keel—KM is known for the draft and trim of the vesselduring the stability test. The metacentric height, GM,ascalculated above, is determined from the inclining experiment.The difference between the height KM and the distance GM isthe height of the center of gravity above the keel, KG. See Fig.4.5.4 Measuring the Angle of Inclination—(See Fig. 5.) Eachtime an inclining weight, W, is shifted a distance, x, the vesselwill settle to some equilibrium heel angle, θ. To measure thisangle, θ, accurately, pendulums or other precise instruments areused on the vessel. When pendulums are used, the two sides ofthe triangle defined by the pendulum are measured. (“Y”) is thelength of the pendulum wire from the pivot point to the battenand (“Z”) is the distance the wire deflects from the referenceposition at the point along the pendulum length where trans-verse deflections are measured. Tangent θ is then calculated:tan θ 5 Z/Y (2)After each weight movement, plotting all of the readings foreach of the pendulums during the inclining experiment aids inthe discovery of bad readings. Since (W)(x)/tan θ should beconstant, the plotted line should be straight. Deviations from astraight line are an indication that there were other momentsacting on the vessel during the inclining. These other momentsmust be identified, the cause corrected, and the weight move-ments repeated until a straight line is achieved. Figs. 6-9illustrate examples of how to detect some of these othermoments during the inclining and a recommended solution foreach case. For simplicity, only the average of the readings isshown on the inclining plots.5.5 Free Surface—During the stability test, the inclining ofthe vessel should result solely from the moving of the incliningweights. It should not be inhibited or exaggerated by unknownmoments or the shifting of liquids on board. However, someliquids will be aboard the vessel in slack tanks so a discussionof “free surface” is appropriate.5.5.1 Standing Water on Deck—Decks should be free ofwater. Water trapped on deck may shift and pocket in a fashionsimilar to liquids in a tank.5.5.2 Tankage During the Inclining—If there are liquids onboard the vessel when it is inclined, whether in the bilges or inthe tanks, it will shift to the low side when the vessel heels.This shift of liquids will exaggerate the heel of the vessel.Unless the exact weight and distance of liquid shifted can beprecisely calculated, the GM from Eq 1 will be in error. Freesurface should be minimized by emptying the tanks completelyFIG. 3 A Typical Incline PlotFIG. 4 Relationship between GM, KM, and KGFIG. 5 Measuring the Angle of InclinationF1321 − 143and making sure all bilges are dry or by completely filling thetanks so that no shift of liquid is possible. The latter method isnot the optimum because air pockets are difficult to removefrom between structural members of a tank, and the weight andcenter of the liquid in a full tank must be accurately determinedto adjust the light ship values accordingly. When tanks must beleft slack, it is desirable that the sides of the tanks be parallelvertical planes and the tanks be regular in shape (that is,rectangular, trapezoidal, and so forth) when viewed fromabove, so that the free surface moment of the liquid can beaccurately determined. The free surface moment of the liquidin a tank with parallel vertical sides can be readily calculatedby the equation:Mfs5 lb3/12Q (3)NOTE 1—Recheck all tanks and voids and pump out as necessary; redoall weight movements and recheck freeboard and draft readings.FIG. 6 Excessive Free LiquidsNOTE 1—Take water soundings and check lines; redo Weight Move-ments 2 and 3.FIG. 7 Vessel Touching Bottom or Restrained by Mooring LinesFIG. 8 Steady Wind From Port Side Came Up After Initial ZeroPoint Taken (Plot Acceptable)NOTE 1—Redo Weight Movements 1 and 5.FIG. 9 Gusty Wind From Port SideF1321 − 144where:Mfs= free surface moment, ft-Ltonsl = length of tank, ft,b = breadth of tank, ft,Q = specific volume of liquid in tank (ft3/ton), and(See Annex A3 for liquid conversions or measure Qdirectly with a hydrometer.)Lton = long ton of 2240 lbs.Free surface correction is independent of the height of thetank in the ship, location of the tank, and direction of heel.5.5.3 As the width of the tank increases, the value of freesurface moment increases by the third power. The distanceavailable for the liquid to shift is the predominant factor. Thisis why even the smallest amount of liquid in the bottom of awide tank or bilge is normally unacceptable and should beremoved before the inclining experiment. Insignificantamounts of liquids in V-shaped tanks or voids (for example, achain locker in the bow), where the potential shift is negligible,may remain if removal of the liquid would be difficult or wouldcause extensive delays.6. Preparations for the Stability Test6.1 General Condition of the Vessel—A vessel should be ascomplete as possible at the time of the stability test. Schedulethe test to minimize th